The steamboat River Queen travels at the rate of 30km/h in still water. If it can travel 45 km up stream in the same amount of time that it takes to go 63 km down stream what is the rate of the current.

Answers

Answer 1

Answer: $x-the\ rate\ of\ the\ current\nt-time\n\n \left\{\begin{array}{ccc}(30-x)t=45\n(30+x)t=63\end{array}\right\n \left\{\begin{array}{ccc}t=(45)/(30-x)\nt=(63)/(30+x)\end{array}\right\n\n(45)/(30-x)=(63)/(30+x)\n\ncross\ multiply\n\n63(30-x)=45(30+x)\n1890-63x=1350+45x\n-63x-45x=1350-1890\n-108x=-540\ \ \ \ /:(-108)\nx=5\n\nAnswer:The\ rate\ of\ the\ current\ is\ 5\ km/h.$

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Choose all the fractions that are equivalent to 4/12.1/3
9/27
5/15
2/8
8/24

Answers

The following fractions that are equivalent to 4/12: 1/3, 9/27, 5/15 and 8/24.

Equivalent Fraction

This classification refers to the fractions that represent the same value even if they are written with different numbers. For finding an equivalent fraction you should simplify the fraction until its simple form.

The given fraction is 4/12, when you divide the numerator and denominator by 4 you find 1/3 which represents the fraction in simplest form .

1/3 is equivalent to 4/12. Because the fraction in simplest form for 4/12 is 1/3 .

9/27 is equivalent to 4/12. Because the fraction in simplest form for 9/27 is 1/3 .

5/15 is equivalent to 4/12. Because the fraction in simplest form for 5/15 is 1/3 .

2/8 is not equivalent to 4/12. Because the fraction in simplest form for 2/8 is 1/4 .

8/24 is equivalent to 4/12. Because the fraction in simplest form for 8/24 is 1/3 .

Read more about equivalent fractions here:

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Answer:

1/3 ! 5/15 ! 8/24 ! 9/27

Step-by-step explanation:

i know math

Provide the reasons for the fol owing proof Given: JK ≅ KL, NK ≅ KM
Prove ΔNKJ ≅ ΔMLK

Statements Reasons

1. JK≅KL,NK≅KM 1. Given

2.
3. ΔNKJ ≅ ΔMLK 3.________

ANSWER CHOICES

a. reflexive property of ≅ ; SAS
b. reflexive property of ≅ ; ASA
c. vertical angles are congruent; ASA
d. vertical angles are congruent; SAS

Answers

Answer:

Option d is correct.

Vertical angles are congruent;

SAS

Step-by-step explanation:

Given: $JK \cong KL$ , $NK \cong KM$

In ΔNKJ and ΔMLK

$JK \cong KL$ and [Side] {Given}

$NK \cong KM$

Vertical angles states that the two lines intersect to make an X, angles on opposite sides of the X are called vertical angles.

i.e $\angle NKJ$ and $\angle MKL$ are vertical angles.

Also, vertical angles are congruent.

$\angle NKJ \cong \angle MKL$ [Angle] [Vertical angles are congruent]

SAS(Side-Angle-Side) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

then, by SAS postulates;

$\triangle NKJ \cong \triangle MLK$ Hence proved!

Therefore:

Statement Reason

1. $JK \cong KL$ , $NK \cong KM$ Given

2. $\angle NKJ \cong \angle MKL$ Vertical angles are congruent

3. $\triangle NKJ \cong \triangle MLK$ SAS

Answer would be D, as the triangles are congruent due to being verticle angles (literally, you can just see theyre the same). Its SAS because you have 2 exact same sides, plus an exact same angle

The histogram shows the duration, in minutes, of movies in theaters. What relationship between the median and mean is shown by the histogram?

The mean is less than the median.
The median is less than the mean.
The mean is equal to the median.
The median and mean cannot be compared from a histogram.

Answers

The correct answer is:

The median is less than the mean.

Explanation:

This histogram is skewed right; the data "peaks" further to the left than the center.

If a histogram is skewed right, the mean is greater than the median.

This is because skewed-right data have a few large values that increase the mean but do not affect where the exact middle of the data is.

Answer:

Option B) The median is less than the mean.

Step-by-step explanation:

We are given the following in the question:

A histogram showing the duration, in minutes, of movies in theaters.

If we observe the shape of the histogram, more values of the histogram lies on the right side, the tail of the distribution is longer on the right hand side than on the left hand side
Hence, the histogram is skewed right.
The histogram is not normal and shows skewness.
It is a right skewed histogram or positively skewed.
Now, for a positively skewed data the mean is greater than the median since more values lies on right side and have a greater value thus the mean increases.
$\text{Mean} > \text{Median}$
The relationship shown by the histogram between mean and median is that median is less than the mean

Smart takes the bus to work. Unfortunately, he forgetshis lunch at home. Clever grabs the lunch and drives
after the bus. The bus has a 15-minute head start and
is traveling at an average rate of 40 mph. Clever is
traveling at an average rate of 60 mph. How long does
Clever take to catch up to the bus? Draw a diagram to
solve the problem.